D.E. Muller and P.E. Schupp. The theory of ends, pushdown automata, and second-order logic. TCS, 37:51--75, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... 1g) be such that ( T ) T , T definable in Lw (MS2S) Does it imply that (T ) is definable in Lw(MS 2 ) N It has been proved in [2] that definable graphs of finite tree width are equationnal, we can find in [1] that equationnal graphs of finite degree are context free (in the sense of [7]) finally, it is proved in [12] that contextfree graphs are definable at the fifth level of the weak MS 2 hierarchy but what about those of infinite tree width It seems to be difficult to apply the above methods in this case, so such a question might require new proof methods; nevertheless the ....

D.E. Muller and P.E. Schupp, The Theory of Ends, Pushdown Automata, and Second-Order Logic, TCS 37 (1985) p 51-75

....expresses a kind of robustness of the notion of regularity wrt. expressiveness and algorithmic complexity under this extension. Finite automata with a stack have raised interest as a kind of infinite reactive systems (then also called pushdown processes) for which various properties are decidable [18, 14, 13, 2, 4, 25, 9], and also in relation with dynamic logics (see, e.g. 11] The decidability results seem surprising; our results may add some intuition why they are possible. Our results have a promising potential for concrete applications to the set based analysis of reactive programs and to the verification ....

D. E. Muller and P. E. Schup. The theory of ends, pushdown automata, and second-order logic. Theoretical Comput. Sci., 37, 1985.

....expresses a kind of robustness of the notion of regularity wrt. expressiveness and algorithmic complexity under this extension. Finite automata with a stack have raised interest as a kind of infinite reactive systems (then also called pushdown processes) for which various properties are decidable [18, 14, 13, 2, 4, 25, 9], and also in relation with dynamic logics (see, e.g. 11] The decidability results seem surprising; our results may add some intuition why they are possible. Our results have a promising potential for concrete applications to the set based analysis of reactive programs and to the verification ....

D. E. Muller and P. E. Schup. The theory of ends, pushdown automata, and second-order logic. Theoretical Comput. Sci., 37, 1985.

....extension CTL . Similar suggestions to extend the expressiveness of CTL are studied in the literature. This includes both the extensions of the path formulas of CTL with regular word automata [VW84,CGK92] and the extension of the state formulas with regular tree automata [MS85] As in the linear framework, one can strengthen these extensions by using more powerful automata, in particular two way and alternating ones. Since it is possible to remove bidirectionality and alternation also in the branching framework [Var98] our treatment of ETL 2a should work here as well. ....

D.E. Muller and P.E. Schupp. The theory of ends, pushdown automata, and secondorder logic. TCS, 37:51--75, 1985.

....containing the context free languages. 1 Introduction When dealing with computers, infinite graphs are natural objects. They emerge naturally in recursive program schemes or communicating automata, for example. Studying them as families of objects is comparatively recent: Muller and Schupp (in [MS 85] first captured the structure of the graphs of pushdown automata, then Courcelle (in [Co 90] defined the set of regular (equational) graphs. More recently Caucal introduced (in [Ca 96] a characterization of graphs in terms of inverse (rational) substitution from the complete binary tree. Step ....

D. Muller and P. Schupp The theory of ends, pushdown automata, and second-order logic, TCS 37, pp. 51--75, 1985.

....graphes rationnels On rational graphs 3 1 Introduction When dealing with computers, innite graphs are natural objects. They emerge naturally in recursive program schemes or communicating automata, for example. Studying them as families of objects is comparatively recent: Muller and Schupp (in [MS 85] rst captured the structure of the graphs of pushdown automata, then Courcelle (in [Co 90] dened the set of regular (equational) graphs. More recently Caucal introduced (in [Ca 96] a characterization of graphs in terms of inverse (rational) substitution from the complete binary tree. Step by ....

D. Muller and P. Schupp The theory of ends, pushdown automata, and second-order logic, TCS 37, pp. 5175, 1985.

....Checking and Higher Order Recursion Hardi Hungar OFFIS, Oldenburg, Germany hungar offis.uni oldenburg.de Abstract. Since Muller and Schupp have shown that monadic secondorder logic is decidable for context free graphs in [MS85], several specialized procedures have been developed for related problems, mostly for sublogics like the modal calculus, or even its alternation free fragment. This work shows the decidability of s1s, the trace version of msol, for the richer set of macro graphs. The generation mechanism of ....

.... are often called contextfree graphs, see [Hab92] It is easily seen that for every regular graph there is a bisimilar macro process of level 1 (modulo the fact that we use vertex labeling instead of edge labeling which makes no essential difference) The same holds for the context free graphs from [MS85]. So it can be said that with the exception of the combination of BPP and BPA from [BEH95] all considered domains are subsumed by macro processes of level 1. As indicated above, the attributes context free, pushdown and regular are used inconsistently in the literature. From our point of view, ....

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D.E. Muller and P.E. Schupp, The theory of ends, pushdown automata, and second-order logic, Theor. Comp. Sc. 37 (1985), 51--75.

....by a path with labels in some rational set. They are easily seen to preserve decidability. The class of graphs is shown to strictly contain the simple graphs 1 among the equational hypergraphs in the sense of Courcelle [9, 12, 11] and the context free graphs in the sense of Muller and Schupp [27] as (natural) special cases. Before we explain the idea of the present article, we review some known facts about equational sets of nite hypergraphs. Basically two sets of operations on hypergraphs have been considered in the literature. The rst was introduced in [5, 11, 10] and corresponds to ....

D. E. Muller and P. E. Schupp, The theory of ends, pushdown automata, and second-order logic, Theoret. Comput. Sci. 37 (1985) 5175.

....VR equational graphs are related to each other. The picture seems to be fairly complete now. Let us add that there is a natural common subclass [8, 9] A simple graph in which every vertex has nite degree is VR equational if and only if it is HR equational. Such graphs are called context free in [26]. A dioeerent description has been given in [7] Almost the same relationships exist between HR equational and VR equational sets of nite graphs. This is no coincidence because every equational graph is the colimit of an equational set of nite hypergraphs equipped with homomorphisms in a ....

D. E. Muller and P. E. Schupp, The theory of ends, pushdown automata, and second-order logic, Theoret. Comput. Sci. 37 (1985) 5175.

.... be such that Gamma1 ( T ) T , T definable in Lw (MS2S) Does it imply that (T ) is definable in Lw(MS 2 ) N It has been proved in [2] that definable graphs of finite tree width are equationnal, we can find in [1] that equationnal graphs of finite degree are context free (in the sense of [7]) finally, it is proved in [12] that contextfree graphs are definable at the fifth level of the weak MS 2 hierarchy but what about those of infinite tree width It seems to be difficult to apply the above methods in this case, so such a question might require new proof methods; nevertheless ....

D.E. Muller and P.E. Schupp, The Theory of Ends, Pushdown Automata, and Second-Order Logic, TCS 37 (1985) p 51-75

....is to consider games over transition graphs of deterministic pushdown automata. Here each node corresponds to a global state of a pushdown automaton, given by the content of the pushdown store and the state of the finite control. These are context free graphs in the sense of Muller and Schupp ([MS85]) also called context free processes in semantics of concurrency, and their unravellings in tree form are the algebraic trees in the sense of [Co83] As Courcelle has shown in [Co94] the monadic second order theory of an algebraic tree is decidable. This result can be applied to games over ....

D.E. Muller, P.E. Schupp, The theory of ends, pushdown automata, and second-order logic, Theor. Comput. Sci. 37 (1985), 51-75.

....that the complete deterministic tree with two successors (two labels) has a decidable monadic theory [Ra 69] we can decide whether a given property expressed by a monadic sentence, is satisfied by the tree . Later Muller and Schupp have extended this decision result to the context free graphs [MS 85] a context free graph is a rooted graph of finite degree which has a finite number of non isomorphic connected components by decomposition by distance from a (any) vertex. These context free graphs are also the transition graphs of pushdown automata [MS 85] Finally Courcelle has shown that ....

....result to the context free graphs [MS 85] a context free graph is a rooted graph of finite degree which has a finite number of non isomorphic connected components by decomposition by distance from a (any) vertex. These context free graphs are also the transition graphs of pushdown automata [MS 85] Finally Courcelle has shown that the monadic theory remains decidable for the equational graphs [Co 90] an equational graph is a graph generated by a deterministic graph grammar. For rooted graphs of finite degree, these equational graphs are the context free graphs [Ca 90] These decision ....

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D. Muller and P. Schupp The theory of ends, pushdown automata, and second-order logic, TCS 37, pp. 51--75, 1985.

....so is the monadic second order theory of M . A different kind of generalization of the Rabin Tree Theorem is concerned with the monadic second order theory of infinite graphs which are regular modifications of trees . A first result in this direction was proved by Muller and Schupp [MS85]; they showed that the monadic second order theory of any context free graph is decidable. These graphs are obtained as transition graphs of pushdown automata (where a vertex is a word qv 2 Q Delta P , for a state set Q and a pushdown alphabet P ) The binary tree arises as a special case, ....

D.E. Muller, P.E. Schupp, The theory of ends, pushdown automata, and second-order logic, Theor. Comput. Sci. 37 (1985), 51-75.

....of the monadic second order (MSO) theory of the full n ary tree (SnS) is among the most widely applied decidability results. Rabin himself [15] inferred a number of decidability results for various mathematical structures interpretable in SnS (e.g. countable linear orders) Muller and Schupp [14] gave rise to the study of graphs de nable in SnS, by showing decidability of the MSO theory of any graph generated by a pushdown automaton; this result was further extended by Courcelle [2] to equational graphs, and by Caucal [1] to pre x recognizable graphs. However, a more sophisticated use ....

D. Muller and P. Schupp. The theory of ends, pushdown automata, and second-order logic. Theoretical Comput. Sci., 37:5175, 1985.

....of the monadic second order (MSO) theory of the full n ary tree (SnS) is among the most widely applied decidability results. Rabin himself [15] inferred a number of decidability results for various mathematical structures interpretable in SnS (e.g. countable linear orders) Muller and Schupp [14] gave rise to the study of graphs de nable in SnS, by showing decidability of the MSO theory of any graph generated by a pushdown automaton; this result was further extended by Courcelle [3] to equational graphs, and by Caucal [2] to pre x recognizable graphs. However, a more sophisticated use ....

D. Muller and P. Schupp. The theory of ends, pushdown automata, and second-order logic. Theoretical Comput. Sci., 37:5175, 1985.

....but in this case we cannot construct a rational transducer, by reducing the undecidable Post s Correspondence Problem [Co 81] A way to consider bisimulation on pushdown transition graphs is to determine their structures. The structure of pushdown transition graphs has been originally studied in [MS 85] Let us give another but effective characterization of these graphs by using graph grammars. We take a set of labels with non null arities. A hyperarc is a word as 1 : s p labelled by a of arity p 0 and joining in order the vertices s 1 ; s p . In particular an arc s a Gamma t ....

D. Muller and P. Schupp The theory of ends, pushdown automata, and second-order logic, TCS 37, pp. 51--75, 1985.

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D.E. Muller and P.E. Schupp. The theory of ends, pushdown automata, and second-order logic. TCS, 37:51--75, 1985.

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D. Muller and P. Schupp. The theory of ends, pushdown automata, and second-order logic. TCS, 37:51--75, 1985.

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